QuaternaryQuartics : Table of Contents

• QuaternaryQuartics -- code to support the paper 'Quaternary Quartic Forms and Gorenstein Rings'
• [QQ] -- Quaternary Quartic Forms and Gorenstein rings (Kapustka, Kapustka, Ranestad, Schenck, Stillman, Yuan, 2021)
• bettiStrataExamples -- a hash table consisting of examples for each of the 19 Betti strata
• Computation of a doubling for each Betti table type -- See Proposition 2.18 in [QQ]
• Count -- an option name
• doubling -- implement the doubling construction
• Doubling Examples -- Doubling of each type of set of points
• Doubling Examples for ideals of 6 points -- For an ideal $I_{\Gamma}$ of six points we compute possible doublings of $I_{\Gamma}$. See Example 2.16 in [QQ] for details
• Example Type [300a] -- An example of an apolar ideal of a quartic that cannot be obtained as a doubling of it's apolar set
• Example Type [300b] -- An example of doubling construction
• Example Type [300c] -- The third family of type [300]
• Finding all possible betti tables for quadratic component of inverse system for quartics in 4 variables -- Material from Section 4 of [QQ]
• Finding the 16 betti tables possible for quartic forms in 4 variables, and examples -- Material from Table 6 and 7 of Appendix 1
• Finding the Betti stratum of a given quartic -- the 19 Betti strata
• Finding the possible betti tables for points in P^3 with given geometry -- Material from Section 3 of [QQ]
• Half canonical degree 20 -- Computation which supports the proof of Proposition 8.4
• Hilbert scheme of 6 points in projective 3-space -- Betti table loci
• Noether-Lefschetz examples -- examples from Section 6.2 in [QQ]
• nondegenerateBorels -- construct all nondegenerate strongly stable ideals of given length
• Normalize -- an option name
• Pfaffians on quadrics -- compute the quartic and betti table corresponding to a pfaffian ideal in a quadric
• pointsIdeal -- create an ideal of points
• quartic -- a quartic given by power sums of linear forms
• quarticType(RingElement) -- the Betti stratum a specific quartic lies on
• random(List,Ideal) -- a random ring element of a given degree
• randomBlockMatrix -- create a block matrix with zero, identity and random blocks
• randomHomomorphism -- create a random homomorphism between graded modules
• randomPoints -- create a matrix whose columns are random points
• Singularities of lifting of type [300b] -- The lifting of [300b] defined by biliaison acquires singularities in dimension 3
• smallerBettiTables -- Find all (potentially) smaller Betti tables that could degenerate to given table
• Type [000], CY of degree 20 -- lifting to a 3-fold with two singular points
• Type [210], CY of degree 18 via linkage -- lifting to a 3-fold with components of degrees 11, 6, 1
• Type [310], CY of degree 17 via linkage -- lifting to a 3-fold with components of degrees 11, 6
• Type [331], CY of degree 17 via linkage -- lifting to a 3-fold with components of degrees 13 and 4
• Type [420], CY of degree 16 via linkage -- lifting to an irreducible 3-fold
• Type [430], CY of degree 16 via linkage -- lifting to a 3-fold with components of degrees 10, 6
• Type [441a], CY of degree 16 -- lifting to a 3-fold with components of degrees 12, 4
• Type [441b], CY of degree 16 -- lifting to a 3-fold with components of degrees 8, 8
• Type [551], CY of degree 15 via linkage -- lifting to a 3-fold with components of degrees 11 and 4
• Type [562] with a lifting of type II, a CY of degree 15 via linkage -- lifting to a 3-fold with components of degrees 7, 4, 4
• Type [562] with lifting of type I, a CY of degree 15 via linkage -- lifting to a 3-fold with components of degree 8, 7
• VSP(F_Q,9) -- Computation appearing in the proof of Theorem 5.16 in [QQ]